In this paper, we adapt Physics-Informed Neural Networks (PINNs) to solve Fisher's equation with solutions characterized by steep traveling wave fronts.We introduce a residual weighting scheme that is based on the underlying reaction dynamics and helps in tracking the propagating wave fronts.Furthermore, we explore a network architecture tailored for solutions in the form of traveling waves. Lastly, we assess the capacity of PINNs to approximate an entire family of traveling wave solutions by incorporating the reaction rate coefficient as an additional input to the network architecture.